A fixed amount of an ideal gas is enclosed in a frictionless piston–cylinder arrangement
CHEMISTRY · Subjective · A Level · Chemistry · Amount of substance · Amount of substance
Problem
A fixed amount of an ideal gas is enclosed in a frictionless piston–cylinder arrangement. Initially the gas is at pressure P1, volume V1 and absolute temperature T1. The piston is slowly moved so that the pressure of the gas becomes 2P1 while, at the same time, its temperature is reduced to 2T1.
(i) Predict qualitatively whether the final volume V2 will be greater than, equal to, or less than the initial volume V1. Give one reason for your answer.
(ii) Show, by treating the gas as ideal, that the ratio of the final volume to the initial volume is V1V2=4T1T1=41.
(iii) Explain physically why the simultaneous change of pressure and temperature leads to the numerical value obtained in part (ii), referring to the roles of both variables in determining the volume of a fixed mass of gas.